| .. _astropy-units: |
|
|
| ************************************** |
| Units and Quantities (`astropy.units`) |
| ************************************** |
|
|
| .. |quantity| replace:: :class:`~astropy.units.Quantity` |
|
|
| .. currentmodule:: astropy.units |
|
|
| Introduction |
| ============ |
|
|
| `astropy.units` handles defining, converting between, and performing |
| arithmetic with physical quantities, such as meters, seconds, Hz, |
| etc. It also handles logarithmic units such as magnitude and decibel. |
|
|
| `astropy.units` does not know spherical geometry or sexagesimal |
| (hours, min, sec): if you want to deal with celestial coordinates, |
| see the `astropy.coordinates` package. |
|
|
| Getting Started |
| =============== |
|
|
| Most users of the `astropy.units` package will :ref:`work with "quantities" |
| <quantity>`: the combination of a value and a unit. The easiest way to create |
| a |quantity| is to simply multiply or divide a value by one of the built-in |
| units. It works with scalars, sequences and Numpy arrays:: |
| |
| >>> from astropy import units as u |
| >>> 42.0 * u.meter # doctest: +FLOAT_CMP |
| <Quantity 42. m> |
| >>> [1., 2., 3.] * u.m # doctest: +FLOAT_CMP |
| <Quantity [1., 2., 3.] m> |
| >>> import numpy as np |
| >>> np.array([1., 2., 3.]) * u.m # doctest: +FLOAT_CMP |
| <Quantity [1., 2., 3.] m> |
|
|
| You can get the unit and value from a |quantity| using the unit and |
| value members:: |
| |
| >>> q = 42.0 * u.meter |
| >>> q.value |
| 42.0 |
| >>> q.unit |
| Unit("m") |
|
|
| From this simple building block, it's easy to start combining |
| quantities with different units:: |
| |
| >>> 15.1 * u.meter / (32.0 * u.second) # doctest: +FLOAT_CMP |
| <Quantity 0.471875 m / s> |
| >>> 3.0 * u.kilometer / (130.51 * u.meter / u.second) # doctest: +FLOAT_CMP |
| <Quantity 0.022986744310780783 km s / m> |
| >>> (3.0 * u.kilometer / (130.51 * u.meter / u.second)).decompose() # doctest: +FLOAT_CMP |
| <Quantity 22.986744310780782 s> |
|
|
| Unit conversion is done using the |
| :meth:`~astropy.units.quantity.Quantity.to` method, which returns a new |
| |quantity| in the given unit:: |
| |
| >>> x = 1.0 * u.parsec |
| >>> x.to(u.km) # doctest: +FLOAT_CMP |
| <Quantity 30856775814671.914 km> |
|
|
| It is also possible to work directly with units at a lower level, for |
| example, to create custom units:: |
| |
| >>> from astropy.units import imperial |
|
|
| >>> cms = u.cm / u.s |
| >>> # ...and then use some imperial units |
| >>> mph = imperial.mile / u.hour |
|
|
| >>> # And do some conversions |
| >>> q = 42.0 * cms |
| >>> q.to(mph) # doctest: +FLOAT_CMP |
| <Quantity 0.939513242662849 mi / h> |
|
|
| Units that "cancel out" become a special unit called the |
| "dimensionless unit": |
|
|
| >>> u.m / u.m |
| Unit(dimensionless) |
|
|
| To create a simple :ref:`dimensionless quantity <doc_dimensionless_unit>`, |
| multiply a value by the unscaled dimensionless unit:: |
| |
| >>> q = 1.0 * u.dimensionless_unscaled |
| >>> q.unit |
| Unit(dimensionless) |
|
|
| `astropy.units` is able to match compound units against the units it already |
| knows about:: |
| |
| >>> (u.s ** -1).compose() # doctest: +SKIP |
| [Unit("Bq"), Unit("Hz"), Unit("3.7e+10 Ci")] |
|
|
| And it can convert between unit systems, such as SI or CGS: |
|
|
| .. doctest-skip:: |
|
|
| >>> (1.0 * u.Pa).cgs |
| <Quantity 10.0 Ba> |
|
|
| The units ``mag``, ``dex`` and ``dB`` are special, being :ref:`logarithmic |
| units <logarithmic_units>`, for which a value is the logarithm of a physical |
| quantity in a given unit. These can be used with a physical unit in |
| parentheses to create a corresponding logarithmic quantity:: |
| |
| >>> -2.5 * u.mag(u.ct / u.s) |
| <Magnitude -2.5 mag(ct / s)> |
| >>> from astropy import constants as c |
| >>> u.Dex((c.G * u.M_sun / u.R_sun**2).cgs) # doctest: +FLOAT_CMP |
| <Dex 4.438067627303133 dex(cm / s2)> |
|
|
| `astropy.units` also handles :ref:`equivalencies <unit_equivalencies>`, such as |
| that between wavelength and frequency. To use that feature, equivalence objects |
| are passed to the :meth:`~astropy.units.quantity.Quantity.to` conversion |
| method. For instance, a conversion from wavelength to frequency doesn't |
| normally work: |
|
|
| >>> (1000 * u.nm).to(u.Hz) # doctest: +IGNORE_EXCEPTION_DETAIL |
| Traceback (most recent call last): |
| ... |
| UnitConversionError: 'nm' (length) and 'Hz' (frequency) are not convertible |
|
|
| but by passing an equivalency list, in this case ``spectral()``, it does: |
|
|
| >>> (1000 * u.nm).to(u.Hz, equivalencies=u.spectral()) # doctest: +FLOAT_CMP |
| <Quantity 2.99792458e+14 Hz> |
|
|
| Quantities and units can be :ref:`printed nicely to strings |
| <astropy-units-format>` using the `Format String Syntax |
| <https://docs.python.org/3/library/string.html#format-string-syntax>`_, the |
| preferred string formatting syntax in recent versions of python. Format |
| specifiers (like ``0.03f``) in new-style format strings will used to format the |
| quantity value:: |
| |
| >>> q = 15.1 * u.meter / (32.0 * u.second) |
| >>> q # doctest: +FLOAT_CMP |
| <Quantity 0.471875 m / s> |
| >>> "{0:0.03f}".format(q) |
| '0.472 m / s' |
|
|
| The value and unit can also be formatted separately. Format specifiers |
| used on units can be used to choose the unit formatter:: |
| |
| >>> q = 15.1 * u.meter / (32.0 * u.second) |
| >>> q # doctest: +FLOAT_CMP |
| <Quantity 0.471875 m / s> |
| >>> "{0.value:0.03f} {0.unit:FITS}".format(q) |
| '0.472 m s-1' |
|
|
| Using `astropy.units` |
| ===================== |
|
|
| .. toctree:: |
| :maxdepth: 2 |
|
|
| quantity |
| standard_units |
| combining_and_defining |
| decomposing_and_composing |
| logarithmic_units |
| format |
| equivalencies |
| conversion |
|
|
| See Also |
| ======== |
|
|
| - `FITS Standard <https://fits.gsfc.nasa.gov/fits_standard.html>`_ for |
| units in FITS. |
|
|
| - The `Units in the VO 1.0 Standard |
| <http://www.ivoa.net/Documents/VOUnits/>`_ for representing units in |
| the VO. |
|
|
| - OGIP Units: A standard for storing units in `OGIP FITS files |
| <https://heasarc.gsfc.nasa.gov/docs/heasarc/ofwg/docs/general/ogip_93_001/>`_. |
|
|
| - `Standards for astronomical catalogues units |
| <http://cds.u-strasbg.fr/doc/catstd-3.2.htx>`_. |
|
|
| - `IAU Style Manual |
| <https://www.iau.org/static/publications/stylemanual1989.pdf>`_. |
|
|
| - `A table of astronomical unit equivalencies |
| <http://www.stsci.edu/~strolger/docs/UNITS.txt>`_ |
|
|
| .. note that if this section gets too long, it should be moved to a separate |
| doc page - see the top of performance.inc.rst for the instructions on how to do |
| that |
| .. include:: performance.inc.rst |
|
|
| Reference/API |
| ============= |
|
|
| .. automodapi:: astropy.units.quantity |
|
|
| .. automodapi:: astropy.units |
|
|
| .. automodapi:: astropy.units.format |
|
|
| .. automodapi:: astropy.units.si |
|
|
| .. automodapi:: astropy.units.cgs |
|
|
| .. automodapi:: astropy.units.astrophys |
|
|
| .. automodapi:: astropy.units.function.units |
|
|
| .. automodapi:: astropy.units.photometric |
|
|
| .. automodapi:: astropy.units.imperial |
|
|
| .. automodapi:: astropy.units.cds |
|
|
| .. automodapi:: astropy.units.equivalencies |
|
|
| .. automodapi:: astropy.units.function |
|
|
| .. automodapi:: astropy.units.function.logarithmic |
| :include-all-objects: |
|
|
| .. automodapi:: astropy.units.deprecated |
|
|
| .. automodapi:: astropy.units.required_by_vounit |
|
|
| Acknowledgments |
| =============== |
|
|
| This code is adapted from the `pynbody |
| <https://github.com/pynbody/pynbody>`__ units module written by Andrew |
| Pontzen, who has granted the Astropy Project permission to use the code |
| under a BSD license. |
|
|
